In his book Rationality, Steven Pinker poses three “simple” math problems:
1) A smart phone and a case cost $110 in total. The phone costs $100 more than the case. How much does the case cost?
2) It takes eight printers eight minutes to print eight brochures. How long would it take 24 printers to print 24 brochures?
3) On a field there is a patch of weeds. Every day the patch doubles in size. It takes 30 days for the patch to cover the whole field. How long did it take for the patch to cover half the field?
According to Pinker, thousands of university students have tried these questions and 83 per cent got at least one wrong while one third got them all wrong.
In case you are wondering, the answers are $5, 8 minutes and 29 days.
The first two questions employ wording which is tricky, but they are the sort of questions we might have a gut feel for.
Unfortunately, our guts can sometimes lead us astray.
The third question is about exponential growth – about doubling curves, for example. On the 29th day, weeds cover 50 per cent of the field which doubles giving 100 per cent coverage the next day.
Understanding exponential growth is integral to many aspects of our lives. Consider COVID-19. The first confirmed death from COVID-19 in the United States was on March 1.
In successive weeks, the numbers grew from two to six to 40 to 264 to 901 to 1,729 deaths per day following an exponential curve. By June 1, 100,000 Americans had died.
Exponential growth is occurring in our fossil fuel consumption and emissions – Canada is three per cent above expectations which means our output will double in 24 years unless we do something.
The world’s population is following an exponential growth curve which is seen in the number of years it takes to add a billion more people to the planet.
The world population hit one billion people in 1804.
It took until 1927 to get to two billion or 123 years. In 2012, we passed the seven billion mark and we will pass eight billion early in 2022, just 10 years later.
These are just a few examples but understanding exponential growth is critical.
